Higher Spin Conformal Geometry in Three Dimensions and Prepotentials for Higher Spin Gauge Fields

TL;DR

This paper develops a conformal geometric framework for higher spin gauge fields in three dimensions, introducing prepotentials that reveal higher spin conformal symmetry and simplify the Hamiltonian formulation.

Contribution

It systematically constructs the conformal geometry for higher spins, defines the Cotton tensor for these fields, and explicitly solves the Hamiltonian constraints for spin 3, with a generalization to all spins in future work.

Findings

Prepotentials exhibit higher spin conformal symmetry.

Explicit solution of constraints for spin 3 fields.

Framework simplifies duality-invariant formulations.

Abstract

We study systematically the conformal geometry of higher spin bosonic gauge fields in three spacetime dimensions. We recall the definition of the Cotton tensor for higher spins and establish a number of its properties that turn out to be key in solving in terms of prepotentials the constraint equations of the Hamiltonian (3 + 1) formulation of four-dimensional higher spin gauge fields. The prepotentials are shown to exhibit higher spin conformal symmetry. Just as for spins 1 and 2, they provide a remarkably simple, manifestly duality invariant formulation of the theory. While the higher spin conformal geometry is developed for arbitrary bosonic spin, we explicitly perform the Hamiltonian analysis and derive the solution of the constraints only in the illustrative case of spin 3. In a separate publication, the Hamiltonian analysis in terms of prepotentials is extended to all bosonic higher spins using the conformal tools of this paper, and the same emergence of higher spin conformal symmetry is confirmed.